Conveners
Free Boundaries in Biology: MS-10-1
- Charles Elbar (Université Claude Bernard Lyon 1)
Free Boundaries in Biology: MS-10-2
- Andrea Poiatti (University of Parma)
Description
Organisers: Charles Elbar, Andrea Poiatti
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Helmut Abels (Universität Regensburg)10/09/2026, 14:00Free Boundaries in Biology
We consider a system consisting of a surface Navier-Stokes equation for incompressible fluids on an elastic inextensible membrane, whose evolution is coupled to the flow of the fluid on the surface. This leads to a highly nonlinear quasilinear geometric evolution equation of parabolic-hyperbolic type. Using a suitable parametrization we linearize the system and obtain well-posedness of it in...
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Mingyue Zhang (TU Wien)10/09/2026, 14:30Free Boundaries in Biology
We study the asymptotic limits of a Keller--Segel system with porous-medium-type nonlinear diffusion and nonlinear logistic sensitivity. We identify three distinguished limits and clarify their connections with the original system. Depending on the parameter regimes, the model converges to a porous medium equation when the chemotactic sensitivity is weak and the chemical diffusion is slow, a...
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Patrik Knopf (Karlsruher Institut für Technologie (KIT))10/09/2026, 15:00Free Boundaries in Biology
I will present a thermodynamically consistent model (from a collaboration with Y. Liu), which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which is determined by a Navier--Stokes equation. In order to take interactions between bulk and boundary into account, we...
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Sebastian Hensel10/09/2026, 15:30Free Boundaries in Biology
The most basic examples of curvature driven interface evolution are gradient flows of the perimeter. I will discuss in this talk, at the example of Mullins-Sekerka flow, how the gradient-flow structure can be used to provide robust solution theories, bypassing the usage of comparison principles typically not available for such problems. I will focus on existence theory based on an energy...
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Theresa Simon (University of Münster)11/09/2026, 09:00Free Boundaries in Biology
I will present an example for how to pass from a first order perimeter optimization problem to a second order curvature optimization problem. While the original model, a nonlocal isoperimetric problem, arises from mathematical physics, its limit is Euler’s elastica functional. This is the 2D analogue of the Willmore energy, which features prominently in the modeling of lipid bilayers....
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Jonas Haselböck (Universität Regensburg)11/09/2026, 09:30Free Boundaries in Biology
In recent years, interface models have become increasingly popular in mathematical biology for describing tumour growth. Among these, the Cahn–Hilliard–Biot model was the first to incorporate both mechanical stress and fluid flow through a heterogeneous, saturated porous medium. In subsequent works, the original model was further extended to include Kelvin–Voigt viscoelasticity. Since the...
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Katharina Hopf11/09/2026, 10:00Free Boundaries in Biology
Viscoelastic phase separation is thought to play an important role in cell biology. Differences in mechanical properties and relaxation times of the constituents can induce dynamic asymmetry during demixing, generating complex morphological transitions such as phase inversion, a characteristic feature of viscoelastic phase separation. In this talk, we determine the interface dynamics arising...
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Elisabetta Rocca (Università di Pavia)11/09/2026, 10:30Free Boundaries in Biology
In this talk we introduce a mathematical model which couples the evolution of a phase-parameter $\varphi$ satisfying a Cahn-Hilliard type relation with the one of an additional variable $\sigma$ influencing the phase separation process. The main application of the model refers to cancer growth processes, where $\sigma$ may represent the concentration of a chemical substance affecting the...
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